## Yield to Maturity The Approximation Approach Outline

Yield to Maturity The Approximation Approach Business 2039

The Approximation FormulaF = Face Value = Par Value = $1,000P = Bond PriceC = the semi annual coupon interestN = number of semi-annual periods left to maturity F – P +C n Semi – annual Y ie ld to M aturity = F + P 2 YTM = 2× s emi – annual Y TM YTM = (1+ s emi – annual Y TM)2 −1

Example Find the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. (Always assume the coupon interest is paid semi-annual y.) Therefore there is coupon interest of $30 paid semi-annual y There are 10 semi-annual periods left until maturity

Example – with solution Find the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. (Always assume the coupon interest is paid semi- annually.) F – P $ 0 , 1 00 − $850 + C + $30 1 $ 5 + $30 n 10 Semi – annual Y iel d to M aturity = = = = 0 0 . 486 F + P 8 , 1 $ 50 9 $ 25 2 2 YTM = 2× s emi – annual Y TM = 0.0486× 2 = 0.09273 = 9.3% YTM = (1+ s emi – annual Y TM)2 −1 = . 1 ( 0486)2 −1 = 9 9 . % 7 The actual answer is 9.87%…so of course, the approximation approach only gives us an approximate answer…but that is just fine for tests and exams.

The logic of the equation The numerator simply represents the average semi-annual returns on the investment…it is made up of two components: The first component is the average capital gain (if it is a discount bond) or capital loss (if it is a premium priced bond) per semi- annual period. The second component is the semi-annual coupon interest received. The denominator represents the average price of the bond. Therefore the formula is basically, average semi-annual return on average investment. Of course, we annualize the semi-annual return so that we can compare this return to other returns on other investments for comparison purposes.